/* Produced by texiweb from libavl.w. */

/* libavl - library for manipulation of binary trees.
   Copyright (C) 1998, 1999, 2000, 2001, 2002, 2004 Free Software
   Foundation, Inc.

   This library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 3 of the License, or (at your option) any later version.

   This library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with this library; if not, write to the Free Software
   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA.
*/

#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "avl.h"

/* Creates and returns a new table
   with comparison function |compare| using parameter |param|
   and memory allocator |allocator|.
   Returns |NULL| if memory allocation failed. */
struct avl_table *
avl_create (avl_comparison_func *compare, void *param,
	    struct libavl_allocator *allocator)
{
	struct avl_table *tree;

	assert (compare != NULL);

	if (allocator == NULL)
		allocator = &avl_allocator_default;

	tree = allocator->libavl_malloc (allocator, sizeof *tree);
	if (tree == NULL)
		return NULL;

	tree->avl_root = NULL;
	tree->avl_compare = compare;
	tree->avl_param = param;
	tree->avl_alloc = allocator;
	tree->avl_count = 0;
	tree->avl_generation = 0;

	return tree;
}

/* Search |tree| for an item matching |item|, and return it if found.
   Otherwise return |NULL|. */
void *
avl_find (const struct avl_table *tree, const void *item)
{
	const struct avl_node *p;

	assert (tree != NULL && item != NULL);
	for (p = tree->avl_root; p != NULL; )
	{
		int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param);

		if (cmp < 0)
			p = p->avl_link[0];
		else if (cmp > 0)
			p = p->avl_link[1];
		else /* |cmp == 0| */
			return p->avl_data;
	}

	return NULL;
}

/* Inserts |item| into |tree| and returns a pointer to |item|'s address.
   If a duplicate item is found in the tree,
   returns a pointer to the duplicate without inserting |item|.
   Returns |NULL| in case of memory allocation failure. */
void **
avl_probe (struct avl_table *tree, void *item)
{
	struct avl_node *y, *z; /* Top node to update balance factor, and parent. */
	struct avl_node *p, *q; /* Iterator, and parent. */
	struct avl_node *n;	/* Newly inserted node. */
	struct avl_node *w;	/* New root of rebalanced subtree. */
	int dir;		/* Direction to descend. */

	unsigned char da[AVL_MAX_HEIGHT]; /* Cached comparison results. */
	int k = 0;		/* Number of cached results. */

	assert (tree != NULL && item != NULL);

	z = (struct avl_node *) &tree->avl_root;
	y = tree->avl_root;
	dir = 0;
	for (q = z, p = y; p != NULL; q = p, p = p->avl_link[dir])
	{
		int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param);
		if (cmp == 0)
			return &p->avl_data;

		if (p->avl_balance != 0)
			z = q, y = p, k = 0;
		da[k++] = dir = cmp > 0;
	}

	n = q->avl_link[dir] =
		tree->avl_alloc->libavl_malloc (tree->avl_alloc, sizeof *n);
	if (n == NULL)
		return NULL;

	tree->avl_count++;
	n->avl_data = item;
	n->avl_link[0] = n->avl_link[1] = NULL;
	n->avl_balance = 0;
	if (y == NULL)
		return &n->avl_data;

	for (p = y, k = 0; p != n; p = p->avl_link[da[k]], k++)
		if (da[k] == 0)
			p->avl_balance--;
		else
			p->avl_balance++;

	if (y->avl_balance == -2)
	{
		struct avl_node *x = y->avl_link[0];
		if (x->avl_balance == -1)
		{
			w = x;
			y->avl_link[0] = x->avl_link[1];
			x->avl_link[1] = y;
			x->avl_balance = y->avl_balance = 0;
		}
		else
		{
			assert (x->avl_balance == +1);
			w = x->avl_link[1];
			x->avl_link[1] = w->avl_link[0];
			w->avl_link[0] = x;
			y->avl_link[0] = w->avl_link[1];
			w->avl_link[1] = y;
			if (w->avl_balance == -1)
				x->avl_balance = 0, y->avl_balance = +1;
			else if (w->avl_balance == 0)
				x->avl_balance = y->avl_balance = 0;
			else /* |w->avl_balance == +1| */
				x->avl_balance = -1, y->avl_balance = 0;
			w->avl_balance = 0;
		}
	}
	else if (y->avl_balance == +2)
	{
		struct avl_node *x = y->avl_link[1];
		if (x->avl_balance == +1)
		{
			w = x;
			y->avl_link[1] = x->avl_link[0];
			x->avl_link[0] = y;
			x->avl_balance = y->avl_balance = 0;
		}
		else
		{
			assert (x->avl_balance == -1);
			w = x->avl_link[0];
			x->avl_link[0] = w->avl_link[1];
			w->avl_link[1] = x;
			y->avl_link[1] = w->avl_link[0];
			w->avl_link[0] = y;
			if (w->avl_balance == +1)
				x->avl_balance = 0, y->avl_balance = -1;
			else if (w->avl_balance == 0)
				x->avl_balance = y->avl_balance = 0;
			else /* |w->avl_balance == -1| */
				x->avl_balance = +1, y->avl_balance = 0;
			w->avl_balance = 0;
		}
	}
	else
		return &n->avl_data;
	z->avl_link[y != z->avl_link[0]] = w;

	tree->avl_generation++;
	return &n->avl_data;
}

/* Inserts |item| into |table|.
   Returns |NULL| if |item| was successfully inserted
   or if a memory allocation error occurred.
   Otherwise, returns the duplicate item. */
void *
avl_insert (struct avl_table *table, void *item)
{
	void **p = avl_probe (table, item);
	return p == NULL || *p == item ? NULL : *p;
}

/* Inserts |item| into |table|, replacing any duplicate item.
   Returns |NULL| if |item| was inserted without replacing a duplicate,
   or if a memory allocation error occurred.
   Otherwise, returns the item that was replaced. */
void *
avl_replace (struct avl_table *table, void *item)
{
	void **p = avl_probe (table, item);
	if (p == NULL || *p == item)
		return NULL;
	else
	{
		void *r = *p;
		*p = item;
		return r;
	}
}

/* Deletes from |tree| and returns an item matching |item|.
   Returns a null pointer if no matching item found. */
void *
avl_delete (struct avl_table *tree, const void *item)
{
	/* Stack of nodes. */
	struct avl_node *pa[AVL_MAX_HEIGHT]; /* Nodes. */
	unsigned char da[AVL_MAX_HEIGHT];    /* |avl_link[]| indexes. */
	int k;				     /* Stack pointer. */

	struct avl_node *p;   /* Traverses tree to find node to delete. */
	int cmp;	      /* Result of comparison between |item| and |p|. */

	assert (tree != NULL && item != NULL);

	k = 0;
	p = (struct avl_node *) &tree->avl_root;
	for (cmp = -1; cmp != 0;
	     cmp = tree->avl_compare (item, p->avl_data, tree->avl_param))
	{
		int dir = cmp > 0;

		pa[k] = p;
		da[k++] = dir;

		p = p->avl_link[dir];
		if (p == NULL)
			return NULL;
	}
	item = p->avl_data;

	if (p->avl_link[1] == NULL)
		pa[k - 1]->avl_link[da[k - 1]] = p->avl_link[0];
	else
	{
		struct avl_node *r = p->avl_link[1];
		if (r->avl_link[0] == NULL)
		{
			r->avl_link[0] = p->avl_link[0];
			r->avl_balance = p->avl_balance;
			pa[k - 1]->avl_link[da[k - 1]] = r;
			da[k] = 1;
			pa[k++] = r;
		}
		else
		{
			struct avl_node *s;
			int j = k++;

			for (;;)
			{
				da[k] = 0;
				pa[k++] = r;
				s = r->avl_link[0];
				if (s->avl_link[0] == NULL)
					break;

				r = s;
			}

			s->avl_link[0] = p->avl_link[0];
			r->avl_link[0] = s->avl_link[1];
			s->avl_link[1] = p->avl_link[1];
			s->avl_balance = p->avl_balance;

			pa[j - 1]->avl_link[da[j - 1]] = s;
			da[j] = 1;
			pa[j] = s;
		}
	}

	tree->avl_alloc->libavl_free (tree->avl_alloc, p);

	assert (k > 0);
	while (--k > 0)
	{
		struct avl_node *y = pa[k];

		if (da[k] == 0)
		{
			y->avl_balance++;
			if (y->avl_balance == +1)
				break;
			else if (y->avl_balance == +2)
			{
				struct avl_node *x = y->avl_link[1];
				if (x->avl_balance == -1)
				{
					struct avl_node *w;
					assert (x->avl_balance == -1);
					w = x->avl_link[0];
					x->avl_link[0] = w->avl_link[1];
					w->avl_link[1] = x;
					y->avl_link[1] = w->avl_link[0];
					w->avl_link[0] = y;
					if (w->avl_balance == +1)
						x->avl_balance = 0, y->avl_balance = -1;
					else if (w->avl_balance == 0)
						x->avl_balance = y->avl_balance = 0;
					else /* |w->avl_balance == -1| */
						x->avl_balance = +1, y->avl_balance = 0;
					w->avl_balance = 0;
					pa[k - 1]->avl_link[da[k - 1]] = w;
				}
				else
				{
					y->avl_link[1] = x->avl_link[0];
					x->avl_link[0] = y;
					pa[k - 1]->avl_link[da[k - 1]] = x;
					if (x->avl_balance == 0)
					{
						x->avl_balance = -1;
						y->avl_balance = +1;
						break;
					}
					else
						x->avl_balance = y->avl_balance = 0;
				}
			}
		}
		else
		{
			y->avl_balance--;
			if (y->avl_balance == -1)
				break;
			else if (y->avl_balance == -2)
			{
				struct avl_node *x = y->avl_link[0];
				if (x->avl_balance == +1)
				{
					struct avl_node *w;
					assert (x->avl_balance == +1);
					w = x->avl_link[1];
					x->avl_link[1] = w->avl_link[0];
					w->avl_link[0] = x;
					y->avl_link[0] = w->avl_link[1];
					w->avl_link[1] = y;
					if (w->avl_balance == -1)
						x->avl_balance = 0, y->avl_balance = +1;
					else if (w->avl_balance == 0)
						x->avl_balance = y->avl_balance = 0;
					else /* |w->avl_balance == +1| */
						x->avl_balance = -1, y->avl_balance = 0;
					w->avl_balance = 0;
					pa[k - 1]->avl_link[da[k - 1]] = w;
				}
				else
				{
					y->avl_link[0] = x->avl_link[1];
					x->avl_link[1] = y;
					pa[k - 1]->avl_link[da[k - 1]] = x;
					if (x->avl_balance == 0)
					{
						x->avl_balance = +1;
						y->avl_balance = -1;
						break;
					}
					else
						x->avl_balance = y->avl_balance = 0;
				}
			}
		}
	}

	tree->avl_count--;
	tree->avl_generation++;
	return (void *) item;
}

/* Refreshes the stack of parent pointers in |trav|
   and updates its generation number. */
static void
trav_refresh (struct avl_traverser *trav)
{
	assert (trav != NULL);

	trav->avl_generation = trav->avl_table->avl_generation;

	if (trav->avl_node != NULL)
	{
		avl_comparison_func *cmp = trav->avl_table->avl_compare;
		void *param = trav->avl_table->avl_param;
		struct avl_node *node = trav->avl_node;
		struct avl_node *i;

		trav->avl_height = 0;
		for (i = trav->avl_table->avl_root; i != node; )
		{
			assert (trav->avl_height < AVL_MAX_HEIGHT);
			assert (i != NULL);

			trav->avl_stack[trav->avl_height++] = i;
			i = i->avl_link[cmp (node->avl_data, i->avl_data, param) > 0];
		}
	}
}

/* Initializes |trav| for use with |tree|
   and selects the null node. */
void
avl_t_init (struct avl_traverser *trav, struct avl_table *tree)
{
	trav->avl_table = tree;
	trav->avl_node = NULL;
	trav->avl_height = 0;
	trav->avl_generation = tree->avl_generation;
}

/* Initializes |trav| for |tree|
   and selects and returns a pointer to its least-valued item.
   Returns |NULL| if |tree| contains no nodes. */
void *
avl_t_first (struct avl_traverser *trav, struct avl_table *tree)
{
	struct avl_node *x;

	assert (tree != NULL && trav != NULL);

	trav->avl_table = tree;
	trav->avl_height = 0;
	trav->avl_generation = tree->avl_generation;

	x = tree->avl_root;
	if (x != NULL)
		while (x->avl_link[0] != NULL)
		{
			assert (trav->avl_height < AVL_MAX_HEIGHT);
			trav->avl_stack[trav->avl_height++] = x;
			x = x->avl_link[0];
		}
	trav->avl_node = x;

	return x != NULL ? x->avl_data : NULL;
}

/* Initializes |trav| for |tree|
   and selects and returns a pointer to its greatest-valued item.
   Returns |NULL| if |tree| contains no nodes. */
void *
avl_t_last (struct avl_traverser *trav, struct avl_table *tree)
{
	struct avl_node *x;

	assert (tree != NULL && trav != NULL);

	trav->avl_table = tree;
	trav->avl_height = 0;
	trav->avl_generation = tree->avl_generation;

	x = tree->avl_root;
	if (x != NULL)
		while (x->avl_link[1] != NULL)
		{
			assert (trav->avl_height < AVL_MAX_HEIGHT);
			trav->avl_stack[trav->avl_height++] = x;
			x = x->avl_link[1];
		}
	trav->avl_node = x;

	return x != NULL ? x->avl_data : NULL;
}

/* Searches for |item| in |tree|.
   If found, initializes |trav| to the item found and returns the item
   as well.
   If there is no matching item, initializes |trav| to the null item
   and returns |NULL|. */
void *
avl_t_find (struct avl_traverser *trav, struct avl_table *tree, void *item)
{
	struct avl_node *p, *q;

	assert (trav != NULL && tree != NULL && item != NULL);
	trav->avl_table = tree;
	trav->avl_height = 0;
	trav->avl_generation = tree->avl_generation;
	for (p = tree->avl_root; p != NULL; p = q)
	{
		int cmp = tree->avl_compare (item, p->avl_data, tree->avl_param);

		if (cmp < 0)
			q = p->avl_link[0];
		else if (cmp > 0)
			q = p->avl_link[1];
		else /* |cmp == 0| */
		{
			trav->avl_node = p;
			return p->avl_data;
		}

		assert (trav->avl_height < AVL_MAX_HEIGHT);
		trav->avl_stack[trav->avl_height++] = p;
	}

	trav->avl_height = 0;
	trav->avl_node = NULL;
	return NULL;
}

/* Attempts to insert |item| into |tree|.
   If |item| is inserted successfully, it is returned and |trav| is
   initialized to its location.
   If a duplicate is found, it is returned and |trav| is initialized to
   its location.  No replacement of the item occurs.
   If a memory allocation failure occurs, |NULL| is returned and |trav|
   is initialized to the null item. */
void *
avl_t_insert (struct avl_traverser *trav, struct avl_table *tree, void *item)
{
	void **p;

	assert (trav != NULL && tree != NULL && item != NULL);

	p = avl_probe (tree, item);
	if (p != NULL)
	{
		trav->avl_table = tree;
		trav->avl_node =
			((struct avl_node *)
			 ((char *) p - offsetof (struct avl_node, avl_data)));
		trav->avl_generation = tree->avl_generation - 1;
		return *p;
	}
	else
	{
		avl_t_init (trav, tree);
		return NULL;
	}
}

/* Initializes |trav| to have the same current node as |src|. */
void *
avl_t_copy (struct avl_traverser *trav, const struct avl_traverser *src)
{
	assert (trav != NULL && src != NULL);

	if (trav != src)
	{
		trav->avl_table = src->avl_table;
		trav->avl_node = src->avl_node;
		trav->avl_generation = src->avl_generation;
		if (trav->avl_generation == trav->avl_table->avl_generation)
		{
			trav->avl_height = src->avl_height;
			memcpy (trav->avl_stack, (const void *) src->avl_stack,
				sizeof *trav->avl_stack * trav->avl_height);
		}
	}

	return trav->avl_node != NULL ? trav->avl_node->avl_data : NULL;
}

/* Returns the next data item in inorder
   within the tree being traversed with |trav|,
   or if there are no more data items returns |NULL|. */
void *
avl_t_next (struct avl_traverser *trav)
{
	struct avl_node *x;

	assert (trav != NULL);

	if (trav->avl_generation != trav->avl_table->avl_generation)
		trav_refresh (trav);

	x = trav->avl_node;
	if (x == NULL)
	{
		return avl_t_first (trav, trav->avl_table);
	}
	else if (x->avl_link[1] != NULL)
	{
		assert (trav->avl_height < AVL_MAX_HEIGHT);
		trav->avl_stack[trav->avl_height++] = x;
		x = x->avl_link[1];

		while (x->avl_link[0] != NULL)
		{
			assert (trav->avl_height < AVL_MAX_HEIGHT);
			trav->avl_stack[trav->avl_height++] = x;
			x = x->avl_link[0];
		}
	}
	else
	{
		struct avl_node *y;

		do
		{
			if (trav->avl_height == 0)
			{
				trav->avl_node = NULL;
				return NULL;
			}

			y = x;
			x = trav->avl_stack[--trav->avl_height];
		}
		while (y == x->avl_link[1]);
	}
	trav->avl_node = x;

	return x->avl_data;
}

/* Returns the previous data item in inorder
   within the tree being traversed with |trav|,
   or if there are no more data items returns |NULL|. */
void *
avl_t_prev (struct avl_traverser *trav)
{
	struct avl_node *x;

	assert (trav != NULL);

	if (trav->avl_generation != trav->avl_table->avl_generation)
		trav_refresh (trav);

	x = trav->avl_node;
	if (x == NULL)
	{
		return avl_t_last (trav, trav->avl_table);
	}
	else if (x->avl_link[0] != NULL)
	{
		assert (trav->avl_height < AVL_MAX_HEIGHT);
		trav->avl_stack[trav->avl_height++] = x;
		x = x->avl_link[0];

		while (x->avl_link[1] != NULL)
		{
			assert (trav->avl_height < AVL_MAX_HEIGHT);
			trav->avl_stack[trav->avl_height++] = x;
			x = x->avl_link[1];
		}
	}
	else
	{
		struct avl_node *y;

		do
		{
			if (trav->avl_height == 0)
			{
				trav->avl_node = NULL;
				return NULL;
			}

			y = x;
			x = trav->avl_stack[--trav->avl_height];
		}
		while (y == x->avl_link[0]);
	}
	trav->avl_node = x;

	return x->avl_data;
}

/* Returns |trav|'s current item. */
void *
avl_t_cur (struct avl_traverser *trav)
{
	assert (trav != NULL);

	return trav->avl_node != NULL ? trav->avl_node->avl_data : NULL;
}

/* Replaces the current item in |trav| by |new| and returns the item replaced.
   |trav| must not have the null item selected.
   The new item must not upset the ordering of the tree. */
void *
avl_t_replace (struct avl_traverser *trav, void *new)
{
	void *old;

	assert (trav != NULL && trav->avl_node != NULL && new != NULL);
	old = trav->avl_node->avl_data;
	trav->avl_node->avl_data = new;
	return old;
}

/* Destroys |new| with |avl_destroy (new, destroy)|,
   first setting right links of nodes in |stack| within |new|
   to null pointers to avoid touching uninitialized data. */
static void
copy_error_recovery (struct avl_node **stack, int height,
		     struct avl_table *new, avl_item_func *destroy)
{
	assert (stack != NULL && height >= 0 && new != NULL);

	for (; height > 2; height -= 2)
		stack[height - 1]->avl_link[1] = NULL;
	avl_destroy (new, destroy);
}

/* Copies |org| to a newly created tree, which is returned.
   If |copy != NULL|, each data item in |org| is first passed to |copy|,
   and the return values are inserted into the tree,
   with |NULL| return values taken as indications of failure.
   On failure, destroys the partially created new tree,
   applying |destroy|, if non-null, to each item in the new tree so far,
   and returns |NULL|.
   If |allocator != NULL|, it is used for allocation in the new tree.
   Otherwise, the same allocator used for |org| is used. */
struct avl_table *
avl_copy (const struct avl_table *org, avl_copy_func *copy,
	  avl_item_func *destroy, struct libavl_allocator *allocator)
{
	struct avl_node *stack[2 * (AVL_MAX_HEIGHT + 1)];
	int height = 0;

	struct avl_table *new;
	const struct avl_node *x;
	struct avl_node *y;

	assert (org != NULL);
	new = avl_create (org->avl_compare, org->avl_param,
			  allocator != NULL ? allocator : org->avl_alloc);
	if (new == NULL)
		return NULL;
	new->avl_count = org->avl_count;
	if (new->avl_count == 0)
		return new;

	x = (const struct avl_node *) &org->avl_root;
	y = (struct avl_node *) &new->avl_root;
	for (;;)
	{
		while (x->avl_link[0] != NULL)
		{
			assert (height < 2 * (AVL_MAX_HEIGHT + 1));

			y->avl_link[0] =
				new->avl_alloc->libavl_malloc (new->avl_alloc,
							       sizeof *y->avl_link[0]);
			if (y->avl_link[0] == NULL)
			{
				if (y != (struct avl_node *) &new->avl_root)
				{
					y->avl_data = NULL;
					y->avl_link[1] = NULL;
				}

				copy_error_recovery (stack, height, new, destroy);
				return NULL;
			}

			stack[height++] = (struct avl_node *) x;
			stack[height++] = y;
			x = x->avl_link[0];
			y = y->avl_link[0];
		}
		y->avl_link[0] = NULL;

		for (;;)
		{
			y->avl_balance = x->avl_balance;
			if (copy == NULL)
				y->avl_data = x->avl_data;
			else
			{
				y->avl_data = copy (x->avl_data, org->avl_param);
				if (y->avl_data == NULL)
				{
					y->avl_link[1] = NULL;
					copy_error_recovery (stack, height, new, destroy);
					return NULL;
				}
			}

			if (x->avl_link[1] != NULL)
			{
				y->avl_link[1] =
					new->avl_alloc->libavl_malloc (new->avl_alloc,
								       sizeof *y->avl_link[1]);
				if (y->avl_link[1] == NULL)
				{
					copy_error_recovery (stack, height, new, destroy);
					return NULL;
				}

				x = x->avl_link[1];
				y = y->avl_link[1];
				break;
			}
			else
				y->avl_link[1] = NULL;

			if (height <= 2)
				return new;

			y = stack[--height];
			x = stack[--height];
		}
	}
}

/* Frees storage allocated for |tree|.
   If |destroy != NULL|, applies it to each data item in inorder. */
void
avl_destroy (struct avl_table *tree, avl_item_func *destroy)
{
	struct avl_node *p, *q;

	assert (tree != NULL);

	for (p = tree->avl_root; p != NULL; p = q)
		if (p->avl_link[0] == NULL)
		{
			q = p->avl_link[1];
			if (destroy != NULL && p->avl_data != NULL)
				destroy (p->avl_data, tree->avl_param);
			tree->avl_alloc->libavl_free (tree->avl_alloc, p);
		}
		else
		{
			q = p->avl_link[0];
			p->avl_link[0] = q->avl_link[1];
			q->avl_link[1] = p;
		}

	tree->avl_alloc->libavl_free (tree->avl_alloc, tree);
}

/* Allocates |size| bytes of space using |malloc()|.
   Returns a null pointer if allocation fails. */
void *
avl_malloc (struct libavl_allocator *allocator, size_t size)
{
	assert (allocator != NULL && size > 0);
	return malloc (size);
}

/* Frees |block|. */
void
avl_free (struct libavl_allocator *allocator, void *block)
{
	assert (allocator != NULL && block != NULL);
	free (block);
}

/* Default memory allocator that uses |malloc()| and |free()|. */
struct libavl_allocator avl_allocator_default =
{
	avl_malloc,
	avl_free
};

#undef NDEBUG
#include <assert.h>

/* Asserts that |avl_insert()| succeeds at inserting |item| into |table|. */
void
(avl_assert_insert) (struct avl_table *table, void *item)
{
	void **p = avl_probe (table, item);
	assert (p != NULL && *p == item);
}

/* Asserts that |avl_delete()| really removes |item| from |table|,
   and returns the removed item. */
void *
(avl_assert_delete) (struct avl_table *table, void *item)
{
	void *p = avl_delete (table, item);
	assert (p != NULL);
	return p;
}
